An orange farmer introduces a new variety of oranges. She states that the mean pH of the new variety is5.2.To test the claim, an independent researcher selected a random sample of28oranges of the new variety and found that the sample mean pH was4.8with a sample standard deviation of0.7.Assume that the population of pH values of the new variety of oranges follow approximately a normal distribution. Complete the parts below to perform a hypothesis test to determine if there is sufficient evidence, at the significance level of0.05, to reject the claim that, the average of the pH of the new variety of oranges, is5.2. (a) Formulate the null hypothesish and the alternative hypothesish that you will use for the test. ho: O x-μ μ yes √no 0<0 OSO ロマロ X X O

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An orange farmer introduces a new variety of oranges. She states that the mean pH of the new variety is5.2.To test the claim, an independent researcher
selected a random sample of28oranges of the new variety and found that the sample mean pH was4.8with a sample standard deviation of0.7.Assume that the
population of pH values of the new variety of oranges follow approximately a normal distribution.
Complete the parts below to perform a hypothesis test to determine if there is sufficient evidence, at the significance level of0.05, to reject the claim thatu, the
average of the pH of the new variety of oranges, is5.2.
(a) Formulate the null hypothesish and the alternative hypothesish that you will use for the test.
ho:0
h₁:0
●
• The value of the test statistic is given byyou
μ
no
0<0 OSO ☐>0
ロミロ
X
X
(b) Perform a hypothesis test. The test statistic has a distributiony(o the test is a testy)o this is other information that will help you with the test.
is the value that delimits an area of 0.025in the right tail.
x-μ
yes
0=0 ☐#0
5
Transcribed Image Text:An orange farmer introduces a new variety of oranges. She states that the mean pH of the new variety is5.2.To test the claim, an independent researcher selected a random sample of28oranges of the new variety and found that the sample mean pH was4.8with a sample standard deviation of0.7.Assume that the population of pH values of the new variety of oranges follow approximately a normal distribution. Complete the parts below to perform a hypothesis test to determine if there is sufficient evidence, at the significance level of0.05, to reject the claim thatu, the average of the pH of the new variety of oranges, is5.2. (a) Formulate the null hypothesish and the alternative hypothesish that you will use for the test. ho:0 h₁:0 ● • The value of the test statistic is given byyou μ no 0<0 OSO ☐>0 ロミロ X X (b) Perform a hypothesis test. The test statistic has a distributiony(o the test is a testy)o this is other information that will help you with the test. is the value that delimits an area of 0.025in the right tail. x-μ yes 0=0 ☐#0 5
Student's t distribution
Step 1: Enter the number of degrees
of freedom.
Step 2: Select one queue or two
queues.
A tail
two tails
Step 3: Enter the critical value(s).
(Round to 3 decimal places.
Step 4: Enter the test statistic.
(Round to 3 decimal places.
3
-2
- 1
0.4+
0.3
0.2 +
0.1
1
2
X
3
Ś
Transcribed Image Text:Student's t distribution Step 1: Enter the number of degrees of freedom. Step 2: Select one queue or two queues. A tail two tails Step 3: Enter the critical value(s). (Round to 3 decimal places. Step 4: Enter the test statistic. (Round to 3 decimal places. 3 -2 - 1 0.4+ 0.3 0.2 + 0.1 1 2 X 3 Ś
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PART B - ***ANSWER IS WRONG

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(b) Perform a hypothesis test. The test statistic has a distributiony(om the test is a testy)o this is other information that will help you with the test.
is the value that delimits an area of0.025 in the right tail.
●
X- μ
• The value of the test statistic is given byyou
Student's t distribution
Step 1: Enter the number of degrees
of freedom.
27
Step 2: Select one queue or two
queues.
A tail
O two tails
Step 3: Enter the critical value(s).
(Round to 3 decimal places.
3.024 2.052
Step 4: Enter the test statistic.
(Round to 3 decimal places.
-3.024
yout 3,024
yes
по
- 2
0.4+
0.3 +
0.2
0.1+
I
I
I
H
I
I
Transcribed Image Text:(b) Perform a hypothesis test. The test statistic has a distributiony(om the test is a testy)o this is other information that will help you with the test. is the value that delimits an area of0.025 in the right tail. ● X- μ • The value of the test statistic is given byyou Student's t distribution Step 1: Enter the number of degrees of freedom. 27 Step 2: Select one queue or two queues. A tail O two tails Step 3: Enter the critical value(s). (Round to 3 decimal places. 3.024 2.052 Step 4: Enter the test statistic. (Round to 3 decimal places. -3.024 yout 3,024 yes по - 2 0.4+ 0.3 + 0.2 0.1+ I I I H I I
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Follow-up Question
(c) Based on your answer to part (b), choose what can be concluded, at the significance level of0.05, about the farmer's statement.
Since the value of the test statistic is in the rejection region, the null hypothesis is rejected. Therefore, there is
sufficient evidence to reject the claim that the mean pH of the new variety of oranges is5.2.
● Since the value of the test statistic is in the rejection region, the null hypothesis is not rejected. Therefore,
there is not enough evidence to reject the claim that the mean pH of the new variety of oranges is5.2.
Since the value of the test statistic is not in the rejection region, the null hypothesis is rejected. Therefore,
there is sufficient evidence to reject the claim that the mean pH of the new variety of oranges is5.2.
O Since the value of the test statistic is not in the rejection region, the null hypothesis is not rejected. Therefore,
there is not enough evidence to reject the claim that the mean pH of the new variety of oranges is5.2.
X
S
Transcribed Image Text:(c) Based on your answer to part (b), choose what can be concluded, at the significance level of0.05, about the farmer's statement. Since the value of the test statistic is in the rejection region, the null hypothesis is rejected. Therefore, there is sufficient evidence to reject the claim that the mean pH of the new variety of oranges is5.2. ● Since the value of the test statistic is in the rejection region, the null hypothesis is not rejected. Therefore, there is not enough evidence to reject the claim that the mean pH of the new variety of oranges is5.2. Since the value of the test statistic is not in the rejection region, the null hypothesis is rejected. Therefore, there is sufficient evidence to reject the claim that the mean pH of the new variety of oranges is5.2. O Since the value of the test statistic is not in the rejection region, the null hypothesis is not rejected. Therefore, there is not enough evidence to reject the claim that the mean pH of the new variety of oranges is5.2. X S
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